Searcharxiv⌕ Search

arXiv subjects

G. C. Bento

Publications and source records attributed to G. C. Bento.

26 records · Page 2Linked to original sources
arXiv2014

Behavioral Traps and the Equilibrium Problem on Hadamard Manifolds

In this paper we present a sufficient condition for the existence of a solution for an equilibrium problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we propose a framework for the convergence analysis of a proximal point algorithm to solve this equilibrium problem in finite time. Finally we offer an application to personal equilibrum problems as behavioral traps problems, using a recent "variational rationality" approach of human behavior.

math.OC↗
arXiv2013

The inexact projected gradient method for quasiconvex vector optimization problems

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is important to have practical solution approaches for computing. In this work, we consider the inexact projected gradient-like method for solving smooth constrained vector optimization problems. Basically, we prove global convergence of any sequence produced by the method to a stationary point assuming that the objective function of the problem is $K$-quasiconvex, instead of the stronger $K$-convexity assumed in the literature.

math.OC↗
arXiv2012

The self regulation problem as an inexact steepest descent method for multicriteria optimization

In this paper, we study an inexact steepest descent method, with Armijo's rule, for multicriteria optimization. The sequence generated by the method is guaranteed to be well-defined. Assuming quasi-convexity of the multicriteria function we prove full convergence of the sequence to a critical Pareto point. As an application, this paper offers a model of self regulation in Psychology, using a recent variational rationality approach.

math.OC↗
arXiv2011

Convergence of inexact descent methods for nonconvex optimization on Riemannian manifolds

In this paper we present an abstract convergence analysis of inexact descent methods in Riemannian context for functions satisfying Kurdyka-Lojasiewicz inequality. In particular, without any restrictive assumption about the sign of the sectional curvature of the manifold, we obtain full convergence of a bounded sequence generated by the proximal point method, in the case that the objective function is nonsmooth and nonconvex, and the subproblems are determined by a quasi distance which does not necessarily coincide with the Riemannian distance. Moreover, if the objective function is $C^1$ with $L$-Lipschitz gradient, not necessarily convex, but satisfying Kurdyka-Lojasiewicz inequality, full convergence of a bounded sequence generated by the steepest descent method is obtained.

math.NA↗
arXiv2010

Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds

In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guaranteed. Under mild assumptions on the multicriteria function, we prove that each accumulation point (if they exist) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming quasi-convexity of the multicriteria function and non-negative curvature of the Riemannian manifold, we prove full convergence of the sequence to a Pareto critical.

math.NA↗
arXiv2010

Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds

In this paper we present the proximal point method for a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.

math.OC↗
arXiv2010

Local Convergence of the Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds

Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.

math.OC↗